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Parmenides was a native of Elea, south of Italy, and flourished in the first half of the fifth century B.C. According to Plato, Socrates in his youth had an interview with Parmenides, then an old man, and learnt much from him. Whether or not this interview is historical, we may at least infer, what is otherwise evident, that Plato himself was influenced by the doctrines of Parmenides. The south Italian and Sicilian philosophers were more inclined to mysticism and religion than those of Ionia, who were on the whole scientific and skeptical(A)/dissenting(B) in their tendencies. But mathematics, under the influence of Pythagoras, flourished more in Magna Graecia than in Ionia; mathematics at that time, however, was fettered(A)/entangled(B) with mysticism. Parmenides was influenced by Pythagoras, but the extent of this influence is disputable(A)/conjectural(B). What makes Parmenides historically important is that he invented a form of metaphysical argument that, in one form or another, is to be found in most subsequent metaphysicians down to and including Hegel. He is often said to have invented logic, but what he really invented was metaphysics based on logic.
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The word here should be the opposite of 'religious' so that it flows with the direction of the sentence. The opposite of religious should be skeptical rather than dissenting which means rebellious. Mathematics can be mixed with mysticism in the sense that some mysticism may accompany mathematics but it cannot be fettered to mysticism which means that it is chained to it and can never escape mystical influences.The author wants to say that the extent of Pythagoras's influence on Parmenides is subject to speculation, i.e., it is conjectural. Disputable is not inaccurate but is less appropriate in this context.

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